Electromagnetic Induction. 



337 



of one coil to the mean circumference of the other — 

 that is, that the product Mc 3 is approximately constant, 

 c being put for sj d l -f x 2 , where a is the mean radius of one 

 of the coils. On closer examination it is seen that this 

 product decreases somewhat from x = to about x = a, and then 

 slowly increases for greater values of x. 



By means of the curve (fig. 1, Plate IX.) it was easy to 

 place the coils A and B so that their coefficient of mutual in- 

 duction might have any desired value within the available 

 range, and thus to assign determinate relative values to 

 the coefficients of mutual induction corresponding to the 

 curves to be traced out by the coils C and D. In Table II. 

 the first wad fourth columns give reference numbers referring 

 to the several curves plotted in fig. 2, PL X., whose coor- 

 dinates are given in Table III.; the third and sixth give the 

 corresponding values of M, the coefficient of mutual induction; 

 and the second and fifth the distance along the scale E F at 

 which the coils A and B had to be clamped in order to obtain 

 these values. 



Table II. 



No. of 

 curve. 



X. 



M. 



No. of 

 curve. 



X. 



M. 



1 



05 



1-0 



2025 



3-72 



5-78 



8-15 



1105 



14-45 



18-7 



24-0 



31-6 



Uncertain. 



Uncertain. 



32-0 



160 



80 



4-0 



20 



1-0 



0-5 



0-25 



0125 

 Zero. 



13 



316 



24-0 

 18-7 

 1445 

 1105 

 8-15 

 5-78 

 3-72 

 2025 



- 0-125 



- 0-25 



- 0-5 



- 1-0 



- 2-0 



- 40 



- 8-0 

 -16-0 

 -32-0 



2 



3 



4 



14 



5 



15 



6 



16 



7 



17 



8 



9 



18 



19 



10 



20 



11 



21 



12 







The position on the scale E F, in which the coil B had to be 

 placed in order to give the required value to the induction- 

 coefficient of any curve, was found by inspecting Table II.; 

 the coil was clamped in the position indicated ; and a number 

 of balancing pairs of positions of the coils C and D were then 

 found. 



In determining the values of the coordinates of the curve 

 of zero induction the coils C and D only were employed. The 

 primary circuit was the same as that in the diagram, 

 omitting the coil A; the secondary circuit was also the 



